Stat 407
Quiz 3
Name
1. For the following data:















T reat X1 X2
1
10 7 


1
11 9 

2
5
6 

2
4
2 

2
5
3 


3
6
8 
3
5
9
(a) (1pt) Calculate the overall mean.
(b) (1pt) Calculate the group means.
(c) (2pts) Break up each observation into its mean, treatment and residual component.
(d) (2pts) Given the between sums of squares (B) and within sums of squares (W) matrices below calculate
the Wilks’ Λ∗ = |W|/|W + B|.
B=
"
44.0 23.7
23.7 36.3
1
#
, W=
"
1.67 2.17
2.17 11.2
#
2. (2pts) For the following plots, which do you think is most likely to have Wilks’ Λ close to 1. Why?
3. (2pts) In testing the hypothesis that the means of two groups are different, you get a p-value equal to 0.05.
If the variance-covariance matrices for the two groups are as follows:
S1 =
"
8 2
2 10
#
, S2 =
"
4 2
2 5
#
would you expect that the true significance of the test statistic is greater than or less than 0.05? Explain.
2